Ohms law and resistivity or electrical conductivity

Consider a cylinder, as shown in Figure 5.1, composed of uniform material, having a length, L, and at each of its ends, a cross-sectional area, A. An electric current, I, defined as the flow rate of electric charge, is applied at one end of the cylinder and exits the other. The cylinder, to a greater or lesser extent, opposes this through-flow of electric current, thereby causing a drop in electric potential, AV, which occurs along the column's length from the end where I enters to the end where I leaves. Electric potential can be described as the potential energy for a unit charge resulting from its position within an electric field. As indicated by Equation (5.1), AV is proportional to I, and the proportionality constant is the resistance, R, which is a characteristic of the cylinder's overall ability to oppose current flow:

The minus sign in Equation (5.1) simply indicates that current flow is in a direction opposite to that of increasing electric potential. Equation (5.1) is referred to as Ohm's law, and the resistance, R, of the cylinder can itself be expressed: 